Related papers: A Poincar\'e Covariant Current Operator for Deep I…
We construct an algebra and a complex of multidifferential operators on tensor products of a Courant algebroid E with values in the endomorphism bundle of a smooth vector bundle B, predual of E, extending the standard complex of the…
A calculation of hadronic timelike form factors in the Poincar\'e-covariant Bethe-Salpeter formalism necessitates knowing the analytic structure of the non-perturbative quark-photon vertex in the context of the Poincar\'e-covariant…
In the heavy quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy quark masses, with coefficients that are functions of the kinematic variable…
The Neumann-Poincar\'{e} operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary integral formulation. Recently, a series expression of the…
This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…
We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some…
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal…
A parameter-free evaluation of the $N - P_{11}(1440)$ electromagnetic transition form factors is performed within a light-front constituent quark model, using for the first time the eigenfunctions of a mass operator which generates a large…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
$^3$He spin-dependent structure functions, $g^3_1(x)$ and $g^3_2(x)$, which parametrize the hadronic tensor in polarized deep-inelastic scattering, were evaluated within the Poincar\'e covariant light-front framework. The Bakamjian-Thomas…
We propose an explicit construction of Poincar\'e operators for the lowest order finite element spaces, by employing spanning trees in the grid. In turn, a stable decomposition of the discrete spaces is derived that leads to an efficient…
This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…
We present a general relativistic framework for the calculation of the electroweak structure of heavy-light mesons within constituent-quark models. To this aim the physical processes in which the structure is measured, i.e. electron-meson…
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
We present a framework which enables the analysis of dynamic inverse problems for wave phenomena that are modeled through second-order hyperbolic PDEs. This includes well-posedness and regularity results for the forward operator in an…
We study the pion electromagnetic and $\gamma^* + \pi^0 \to \gamma$ transition form factors at intermediate momentum transfer. We calculate soft, nonperturbative corrections to the leading perturbative amplitudes which arise from the $q\bar…
A study of the deuteron structure in the framework of relativistic quantum mechanics is presented. Point-form (PF) relativistic quantum mechanics (RQM) is applied to the elastic eD scattering. The deuteron wave function and neutron form…
A Poincare-invariant description of mesonic baryon resonance decays is presented following the point form of relativistic quantum mechanics. In this contribution we focus on pionic decay modes. It is found that the theoretical results in…
We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery…
A general procedure for constructing conserved electromagnetic current operators, for both finite and infinite degree of freedom systems, is given. A four-momentum operator consisting of matter, photon, and electromagnetic interactions is…